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A074025 Numbers n such that a triplewhist tournament TWh(n) exists. 2
1, 4, 8, 16, 99999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The term a(5) = 99999999999999999999 is a fake, inserted to prevent this sequence being incorrectly returned by Superseeker. Of course it will be replaced by the correct value, once that is determined.

The present state of knowledge, quoting from Ge & Lam and the link below, is that a TWh(n) exists iff n == 0 or 1 (mod 4), except for n = 5, 9, 12 and possibly excepting n in {17, 57, 65, 69, 77, 85, 93, 117, 129, 153}.

After 16, the sequence continues 17?, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57?, ...

REFERENCES

G. Ge and C. W. H. Lam, Some new triplewhist tournaments TWh(v), J. Combinat. Theory, A101 (2003), 153-159.

LINKS

Table of n, a(n) for n=1..5.

Harri Haanpää and Petteri Kaski, The near resolvable 2-(13,4,3) designs and thirteen-player whist tournaments, [shows that no TWh(13) exists]

CROSSREFS

Sequence in context: A241197 A130436 A260306 * A031462 A045066 A151911

Adjacent sequences:  A074022 A074023 A074024 * A074026 A074027 A074028

KEYWORD

nonn,more,nice

AUTHOR

N. J. A. Sloane, Oct 16 2003

EXTENSIONS

Of course this entry is much too short. But I have included it in the hope that this will encourage someone to settle the question of whether a(5) is 17 or 20 - i.e., does a TWh(17) exist?

Link supplied by Jon E. Schoenfield, Aug 01 2006

STATUS

approved

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Last modified February 20 18:29 EST 2018. Contains 299381 sequences. (Running on oeis4.)